Binary to decimal conversion Convert the binary number 01001110₂ to decimal (base 10).

Introduction / Context:
Converting binary to decimal requires summing the place values where bits are 1. This reinforces understanding of positional notation in base 2.

Given Data / Assumptions:

• Binary: 01001110₂.
• Bit weights from MSB to LSB: 128, 64, 32, 16, 8, 4, 2, 1.

Concept / Approach:
Add the weights corresponding to the 1 bits in the binary string to obtain the decimal value.

Step-by-Step Solution:

Verification / Alternative check:
Interpret as hex first: 0100 1110₂ = 0x4E; convert 0x4E = 4*16 + 14 = 64 + 14 = 78.

Why Other Options Are Wrong:

• 4E: That is the hexadecimal form, not decimal.
• 76 / 116: Sum of selected weights does not equal these numbers for this bit pattern.

Common Pitfalls:
Misaligning bit weights, confusing hex representation with decimal value, or forgetting the leading zero does not change value.

Final Answer:
78